Publication

Gaussian upper density estimates for spatially homogeneous SPDEs

2012
Reports

Abstract

We consider a general class of SPDEs in mathbb{R}^d driven by a Gaussian spatially homogeneous noise which is white in time. We provide sufficient conditions on the coefficients and the spectral measure associated to the noise ensuring that the density of the corresponding mild solution admits an upper estimate of Gaussian type. The proof is based on the formula for the density arising from the integration-by-parts formula of the Malliavin calculus. Our result applies to the stochastic heat equation with any space dimension and the stochastic wave equation with d\in {1,2,3}. In these particular cases, the condition on the spectral measure turns out to be optimal.

Official source

https://infoscience.epfl.ch/entities/publication/6e862e3f-0fd5-4568-b51e-e14e0cc84d5c

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2012
Reports

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/6e862e3f-0fd5-4568-b51e-e14e0cc84d5c

About this result

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Gaussian upper density estimates for spatially homogeneous SPDEs

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